A new collocation method for approximate solution of the pantograph functional differential equations with proportional delay

The paper presents a new numerical method for solving functional differential equations with proportional delays of the first and higher orders. The method consists of replacing the initial equation by an approximate equation which has an exact analytic solution with a set of free parameters. These free parameters are determined by the use of the collocation procedure. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results. The numerical results show that the proposed method is of a high accuracy and is efficient for solving a wide class of functional-differential equations with proportional delays including equations of neutral type. The method is applicable to both initial and boundary value problems.

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